Question: Simplify the following expression: $ t = \dfrac{-2k + 8}{-9} + \dfrac{-9}{2} $
Answer: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{2}{2}$ $ \dfrac{-2k + 8}{-9} \times \dfrac{2}{2} = \dfrac{-4k + 16}{-18} $ Multiply the second expression by $\dfrac{-9}{-9}$ $ \dfrac{-9}{2} \times \dfrac{-9}{-9} = \dfrac{81}{-18} $ Therefore $ t = \dfrac{-4k + 16}{-18} + \dfrac{81}{-18} $ Now the expressions have the same denominator we can simply add the numerators: $t = \dfrac{-4k + 16 + 81}{-18} $ $t = \dfrac{-4k + 97}{-18}$ Simplify the expression by dividing the numerator and denominator by -1: $t = \dfrac{4k - 97}{18}$